I've got both FFX and FFX International but I started playing on the regular and now a few hours into the game I realized that I actually want to play it in Japanese. Will it work to just switch to International and continue or do I then have to start over?
If not, is there a way for me to just change the language?

Think he saying change the system language to Japanese could be wrong. I Pretty sure that wont work that will just change the system language. Unless the game has built in option for language switching most likely gona have to use version of the game that supports the language you want and the saves will not be compatible.